6y+3x=9

Subtract 3x from both sides of the equation.

6y=9-3x

Divide each term by 6 and simplify.

Divide each term in 6y=9-3x by 6.

6y6=96+-3×6

Cancel the common factor of 6.

Cancel the common factor.

6y6=96+-3×6

Divide y by 1.

y=96+-3×6

y=96+-3×6

Simplify each term.

Cancel the common factor of 9 and 6.

Factor 3 out of 9.

y=3(3)6+-3×6

Cancel the common factors.

Factor 3 out of 6.

y=3⋅33⋅2+-3×6

Cancel the common factor.

y=3⋅33⋅2+-3×6

Rewrite the expression.

y=32+-3×6

y=32+-3×6

y=32+-3×6

Cancel the common factor of -3 and 6.

Factor 3 out of -3x.

y=32+3(-x)6

Cancel the common factors.

Factor 3 out of 6.

y=32+3(-x)3(2)

Cancel the common factor.

y=32+3(-x)3⋅2

Rewrite the expression.

y=32+-x2

y=32+-x2

y=32+-x2

Move the negative in front of the fraction.

y=32-x2

y=32-x2

y=32-x2

y=32-x2

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Reorder 32 and -x2.

y=-x2+32

Rewrite in slope-intercept form.

y=-12x+32

y=-12x+32

Find the values of m and b using the form y=mx+b.

m=-12

b=32

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: -12

y-intercept: 32

Slope: -12

y-intercept: 32

Choose 1 to substitute in for x to find the ordered pair.

Replace the variable x with 1 in the expression.

f(1)=-12+32

Simplify the result.

Combine the numerators over the common denominator.

f(1)=-1+32

Add -1 and 3.

f(1)=22

Divide 2 by 2.

f(1)=1

The final answer is 1.

1

1

The y value at x=1 is 1.

y=1

y=1

Choose 3 to substitute in for x to find the ordered pair.

Replace the variable x with 3 in the expression.

f(3)=-32+32

Simplify the result.

Add -32 and 32.

f(3)=0

The final answer is 0.

0

0

The y value at x=3 is 0.

y=0

y=0

Create a table of the x and y values.

xy1130

xy1130

Graph the line using the slope and the y-intercept, or the points.

Slope: -12

y-intercept: 32

xy1130

Graph 6y+3x=9